The Chemical Potential of Water

The chemical potential of the solvent in a solution may be altered by changing the temperature and external pressure applied to the solution and by changing the mole fraction of the solute in the solution. For a homogeneous solution the change in chemical potential of the solvent is expressed as $$d{\mu _1}\, = \, - {\bar S_1}dt\, + \,{\bar V_1}dp\, + \,{{\partial {\mu _1}} \over {\partial {x_2}}}d{x_2}$$ (5) a thermodynamic statement which was derived as Eq. (5) in Chapter II. If the temperature and the externally applied pressure are held constant while changing the mole fraction from x2 = O for pure solvent to \({x_2}\, = \,{{{n_2}} \over {{n_1} + {n_1}}}\) for the solution, then the total change in the chemical potential of the solvent for this homogeneous solution becomes $$\Delta {\mu _1}\, = \,{\int {d\mu } _1}\, = \,\int_{{x_{2\,}} = \,\,o}^{{x_{2\, = \,{{{n_2}} \over {{n_{1\,}} + {n_2}}}}}} {{{\partial {\mu _1}} \over {\partial {x_2}}}} d{x_2}.$$